Question

A simple pendulum of length 1m makes 400 complete oscillations in 8s at a certain place. If another pendulum makes 100 complete oscillation in 1s at the same place.
Find the length of the second pendulum.

Answer 1

The period:

$$T=2\pi\sqrt{\frac{l}{g}}$$

$$T_1=\frac{8}{400}=0.02\ s,T_2=\frac{1}{100}=0.01\ s$$

Thus,

$$l_2=l_1\left(\frac{T_2}{T_1}\right)^2=1\left(\frac{0.02}{0.01}\right)^2=4\ m$$